Research and development of semiconductor devices in which silicon carbide is used as a semiconductor material instead of silicon is now being actively performed. Among the silicon carbide semiconductor devices, MOSFET is of particular interest (see for example Japanese Patent Laying-Open No. 2009-158933 (hereinafter referred to as PTL 1)). PTL 1 discloses that an epitaxial film made of silicon carbide is formed on a surface of a silicon carbide substrate, and an oxide film is thereafter formed on a surface of the epitaxial film. After this, an annealing process is performed in a nitrogen-containing atmosphere, and another annealing process is further performed using argon gas as an atmosphere. According to PTL 1, such processes can be performed to reduce the interface state density in a boundary region between the epitaxial film and the oxide film and consequently increase the carrier mobility in the epitaxial film.